1. Field of the Invention
This invention relates to improving the signal-to-noise ratio of a digital communication system suffering from intersymbol interference.
2. Background
The dramatic increase in desktop computing power driven by intranet-based operations and the increased demand for time-sensitive delivery between users has spurred development of high speed Ethernet LANs. 100BASE-TX Ethernet, using existing Category 5 copper wire, and the newly developing 1000BASE-T Ethernet for Gigabit/s transfer of data over Category 5 copper wire require new techniques in high speed symbol processing. In addition, high speed processing of data is in demand for use with existing switching boards which may currently be required to process data at a rate of 1000 Mb/s per port. Gigabit per second transfer can be accomplished utilizing four twisted pairs and a 125 megasymbol/s transfer rate on each pair where each symbol represents two bits.
Physically, data is transferred using a set of voltages where each voltage represents one or more bits of data. Each voltage in the set is referred to as a symbol and the whole set of voltages is referred to as a symbol alphabet.
One system of transferring data at high rates is Non Return to Zero (NRZ) signaling. In NRZ, the symbol alphabet {A} is {-1, +1}. A logical "1" is transmitted as a positive voltage while a logical "0" is transmitted as a negative voltage. At 125 M symbols/s, the pulse width of each symbol (the positive or negative voltage) is 8 ns.
An alternative modulation method for high speed symbol transfer is MLT3 and involves a three level system. (See American National Standard Information system, Fibre Distributed Data Interface (FDDI)--Part: Token Ring Twisted Pair Physical Layer Medium Dependent (TP-PMD), ANSI X3.263:199X). The symbol alphabet for MLT3 is {A}={-1, 0, +1}. In MLT3 transmission, a logical 1 is transmitted by either a -1 or a +1 while a logic 0 is transmitted as a 0. A transmission of two consecutive logic "1"s does not require the system to pass through zero in the transition. A transmission of the logical sequence ("1", "0", "1") would result in transmission of the symbols (+1, 0, -1) or (-1, 0, +1) depending on the symbols transmitted prior to this sequence. If the symbol transmitted immediately prior to the sequence was a +1, then the symbols (+1, 0, -1) are transmitted. If the symbol transmitted before this sequence was a -1, then the symbols (-1, 0, +1) are transmitted. If the symbol transmitted immediately before this sequence was a 0, then the first symbol of the sequence transmitted will be a +1 if the previous logical "1" was transmitted as a -1 and will be a -1 if the previous logical "1" was transmitted as a +1.
The detection system in the MLT3 standard, however, needs to distinguish between 3 levels, instead of two levels in a more typical two level system. The signal to noise ratio required to achieve a particular bit error rate is higher for MLT3 signaling than for two level systems. The advantage of the MLT3 system, however, is that the energy spectrum of the emitted radiation from the MLT3 system is concentrated at lower frequencies and therefore more easily meets FCC radiation emission standards for transmission over twisted pair cables. Other communication systems may use a symbol alphabet having more than two voltage levels in the physical layer in order to transmit multiple bits of data using each individual symbol.
A block diagram of a typical digital communication transmission system is illustrated in FIG. 1A. In FIG. 1A, the transmitted data is represented by the symbol sequence {a.sub.k }. The transmitted symbols in the sequence {a.sub.k } are members of the symbol alphabet {A}. In the case of two level NRZ signaling, the symbol alphabet {A} is given by {-1, +1}. The index k represents the time index for that symbol, i.e. at sample time k, the symbol being transmitted is given by a.sub.k. The channel response is represented by the channel function f(z). The signal, x.sub.k, is summed with the noise sample n.sub.k to represent the random noise on the transmission line. The signal, suffering from both the channel distortion and the random noise, is input to the detector.
For the sake of simplicity, a baseband transmission system is assumed, although the techniques shown are easily extended to a passband transmission system. (See E. A. LEE AND D. G. MESSERCHMITT, DIGITAL COMMUNICATIONS (1988)) It is also assumed that the channel model includes the effect of transmit and receive filtering. In addition, the transmission channel is assumed to be linear in that two overlapping signals simply add as a linear superposition. Therefore, the channel function polynomial can be defined as EQU f(Z)=f.sub.0 +f.sub.1 Z.sup.-1 +f.sub.2 Z.sup.-2 + . . . +f.sub.N Z.sup.-N,(1)
where f.sub.0, . . . , f.sub.j, . . . , f.sub.N are the polynomial coefficients representing the dispersed component of the (k-j)th symbol present in the a.sub.k th symbol and N is a cut-off integer such that f.sub.j for j&gt;N is negligible. The polynomial f(Z) represents the Z-transformation of the frequency response of the transmission channel. (Z.sup.-1 represents a one period delay) See A. V. OPPENHEIM & R. W. SCHAFER, DISCRETE-TIME SIGNAL PROCESSING 1989.
The noiseless output of the channel at sample time k is then given by EQU x.sub.k =f.sub.0 *a.sub.k +f.sub.1 *a.sub.k-1 + . . . f.sub.N *a.sub.k-N,(2 )
where, without loss of generality, fo can be assumed to be 1. Thus, the channel output signal at time k depends, not only on transmitted data at time k, but past values of the transmitted data. This effect is known as "intersymbol interference" (ISI). See LEE & MESSERSCHMITT.
Intersymbol interference is a result of the dispersive nature of the communication channel. The IEEE LAN standards require that systems be capable of transmitting and receiving data through at least a 100 meter cable. FIG. 1C shows a transmission bit stream with the effects of dispersion. FIG. 1D shows the power spectrum of the dispersed pulse with frequency. In a 100 meter cable, the signal strength at the Nyquist frequency of 62.5 Mhz is reduced nearly 20 db at the receiving end of the cable. Given this dispersion, a single symbol may affect symbols throughout the wire.
The noise element of the signal is represented by the sequence {n.sub.k }. Therefore, the noisy output of the channel is given by EQU y.sub.k =x.sub.k +n.sub.k, (3)
where the noise samples {n.sub.k } are assumed to be independent and identically distributed Gaussian random variables (see LEE & MESSERSCHMITT) with variance equal to .sigma..sup.2.
Most state-of-the art communication systems use two types of detectors for combating the ISI described by equation (2). These two detectors, Linear Equalization and Decision Feedback Equalization, are shown in FIG. 1B.
A liner equalizer having m+1 multipliers is illustrated in FIG. 2. In FIG. 2, the symbol Y.sub.k is inputted to a delay array 10 having delays (D.sub.1 through D.sub.m) which, at each stage, delay the symbol by one time period. A set of multipliers 20 having multipliers M.sub.0 through M.sub.m multiply each of the m+1 symbols in the array of delays D.sub.1 through D.sub.m by a corresponding coefficient C.sub.0 through C.sub.m. The adder 30 adds together the outputs of multipliers M.sub.0 -M.sub.m to obtain the resulting signal EQU a.sub.k '=C.sub.0 y.sub.k +C.sub.1 y.sub.k-1 + . . . +C.sub.m y.sub.k-m.(4)
The signal a.sub.k ' from the linear equalizer is inputted to decider 40 which decides on the output symbol a.sub.k. The output symbol a.sub.k is the symbol from the symbol alphabet {A} which best approximates the input signal a.sub.k '.
The multiplier coefficients, C.sub.0 through C.sub.m, define a transfer function T given by EQU T=C.sub.0 +C.sub.1 Z.sup.-1 + . . . +C.sub.m Z.sup.-m. (5)
The coefficients C.sub.0 through C.sub.m may be chosen by an intelligent algorithm in an adaptive chip in order optimize the functioning of the equalizer. A zero-forcing linear equalizer (ZFLE) has a transfer function T given by the inverse of the frequency response of the channel. A minimum mean squared error based linear equalizer (MMSE-LE) optimizes the mean squared error between the transmitted data and the detected data, and hence finds a compromise between the un-canceled ISI at the output terminal of the equalizer and the noise variance.
The primary disadvantage of a linear equalizer is that, while removing the ISI due to the channel, it also causes the noise to be enhanced. This is especially true in a channel like the twisted copper pair channel, where the frequency response of the channel has significant attenuation across the transmitted signal bandwidth. Hence, in twisted-pair channels (which are commonly used in applications such as 10/100/1000BASE-TX Ethernet and digital subscriber loops), the noise {n.sub.k } may be enhanced by the linear equalizer detector, reducing noise immunity.
FIG. 3 illustrates a Decision Feedback Equalizer (DFE) with N.sub.ff multipliers in the feed-forward filter and N.sub.fb multipliers in the feedback filter. The input signal y.sub.k is inputted to the feed-forward filter 100. The resulting signal is added with the resulting signal from the feed-back filter 200 in adder 300. The added signal is inputted to circuit 400 which determines the output a.sub.k symbol of the equalizer.
In feed-forward filter 100, the input signal y.sub.k is inputted to a feed-forward delay array having delays D.sub.1.sup.ff through D.sub.ff-1.sup.ff. Each delay delays the signal by one period so that the delay array 101 stores N.sub.ff -1 past input signals. Each of the stored signals is multiplied by a corresponding coefficient C.sub.0 through C.sub.Nff-1 by multipliers M.sub.0.sup.ff through M.sub.nff-1.sup.ff. The results of each of the multipliers M.sub.0.sup.ff through M.sub.nff-1.sup.ff are added together in adder 103 so that the signal inputted to adder 300 on line 301 is given by EQU a.sub.k '=C.sub.0 y.sub.k +C.sub.1 y.sub.k-1 + . . . +C.sub.Nff-1 y.sub.k-Nff+1. (6)
The feed-back filter 200 inputs the output symbol a.sub.k to a feed-back delay array 201 having delays D.sub.0.sup.fb through D.sub.Nfb-1.sup.fb. The feed-back delay array 201 stores N.sub.fb-1 past determined symbols, a.sub.k-Nfb+1 through a.sub.k-1. The output symbols of the feed back delay array 201 are inputted to multipliers 202, M.sub.0.sup.fb through M.sub.Nfb-1.sup.fb respectively. The resulting signals from multipliers 202 are added in adder 203 so that the input signal of adder 300 on line 302 is given by EQU a.sub.k "=b.sub.0 a.sub.k-1 +b.sub.1 a.sub.k-2 +b.sub.Nfb-1 a.sub.k-Nfb+1.(7)
Adder 300 adds the input signal on line 301 with the negative of the input signal on line 302 to obtain a.sub.k '-a.sub.k " which is received by decider 400. Decider 400 decides on the output symbol a.sub.k. The output symbol a.sub.k arrived at by decider 400 is the symbol in symbol alphabet {A} which most closely approximates the signal a.sub.k '-a.sub.k " at the input terminal of decider 400.
The DFE operates on the principle that if the past transmitted data is correctly detected, then the ISI effect of these past data symbols can be canceled from the current received signal prior to detection. For a zero-forcing DFE, the feed-forward finite impulse response filter (FF-FIR) transfer function is set to 1 (i.e., C.sub.0 =1 and C.sub.1 through C.sub.m are 0), and the feedback FIR (FB-FIR) transfer function is given by [f(z)-1], f(z) being the channel function.
Since past detected data samples contain no noise, DFE does not suffer from noise enhancement. However, DFE suffers from error propagation. If one of the past detected symbols is incorrect, then the effects of that error propagate to more symbol decisions in the future.
In addition, the DFE has the disadvantage that the sample power contained in the dispersive power of the channel, and represented by the ISI coefficients, is discarded prior to detection of the current symbol and therefore wasted. More precisely, the system has information regarding the current transmitted data symbol in the prior received signals which DFE does not utilize.
Also, because the equalizer is a feedback equalizer, pipelining of the feedback filtering operation is not possible, unlike a linear equalizer whose operation can be pipelined. Yet another disadvantage of a DFE versus a linear equalizer is that a linear equalizer depends only on past input signals to the detector while a DFE depends on past output symbols.